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Brain Injury Turns Man Into Math Genius

mpicpp sends in the story of Jason Padgett, a man who developed extraordinary mathematical abilities as the result of brain trauma when he was attacked outside a bar. "Padgett, a furniture salesman from Tacoma, Wash., who had very little interest in academics, developed the ability to visualize complex mathematical objects and physics concepts intuitively. The injury, while devastating, seems to have unlocked part of his brain that makes everything in his world appear to have a mathematical structure 'I see shapes and angles everywhere in real life' — from the geometry of a rainbow, to the fractals in water spiraling down a drain, Padgett told Live Science." "He describes his vision as 'discrete picture frames with a line connecting them, but still at real speed.' If you think of vision as the brain taking pictures all the time and smoothing them into a video, it's as though Padgett sees the frames without the smoothing. "

208 comments

  1. No story here, move along by Bryan+Ischo · · Score: 5, Interesting

    Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?

    A google search reveals a history of his story popping up from time to time - probably whenever he can find a venue to promote himself, and whenever sites like Slashdot get duped into posting about him - but I found nothing that describes anything that he's actually able to intuit about math since this injury other than a bunch of crap about how he can 'see mathematical patterns' now. Awesome - so how about parlaying that into any statement that demonstrates any extraordinary grasp of math? Because in all my searching, I haven't found this dude to have ever said anything that anyone couldn't easily just make up.

    I also found this comical link to "End of Pi Found" on some Physics forum:

    http://lofi.forum.physorg.com/...

    Not sure if it's the same guy but it was posted by a Jason Padgett who says he is a "math/physics student in Washington state", and the Jason Padgett in the article is supposedly from Tacoma, Washington. Note that the post was from 2008 and the article that Slashdot has linked to describes Padgett as a "sophomore in college". Some math genius - still a sophomore in college 6 years later!

    Slashdot, why do you waste my time with this crap?

    I swear, Slashdot editors are worse than the patent office; they don't do even he smallest amount of verification before rubber stamping what is presented to them and pushing it out.

    1. Re:No story here, move along by ColdWetDog · · Score: 0

      I swear, Slashdot editors are worse than the patent office; they don't do even he smallest amount of verification before rubber stamping what is presented to them and pushing it out.

      You must be new here.

      --
      Faster! Faster! Faster would be better!
    2. Re:No story here, move along by kruach+aum · · Score: 2

      I was going to post something like this but less involved. This dude is being called a savant for no reason, as he does not actually inhibit any savant-like skills, or really any skills at all. The only concrete detail I was able to find is that he once drew a pattern of triangles in a circle.

    3. Re:No story here, move along by TeknoHog · · Score: 1

      I was also wondering how much this seeing ability contributes to actual, productive math ability. The visions described remind me of what, erm, some people see when on acid.

      I'm particularly interested in the idea, being mathematically minded myself, and I believe my ability to conceptualize things in many visual dimensions is an important factor. Nevertheless, there is rarely a direct translation from my pictorial musings into hard and solid math. Visualization helps you get new ideas, but it's implementing them in some rigorous language that's the hard part. I guess it's the linguistic tendencies that might help there...

      --
      Escher was the first MC and Giger invented the HR department.
    4. Re:No story here, move along by Anonymous Coward · · Score: 0

      That forum link seems to be genuine as the guys appears to be obsessed with pi. I guess that if you believe you are genius, you are or at least there's an app for that.

    5. Re: No story here, move along by alex4u2nv · · Score: 1

      Looks like his human graphics card was fried.
      I guess calling yourself math and physics intuitive is a good way of coping with 8th graphics and no 3d driver :)

    6. Re:No story here, move along by geekoid · · Score: 1

      No one else does it, it's another way to look how parts of the brain function.
      Acquired savant syndrome is an interesting subject.

      I wouldn't call a guy who sees angles and connected shapes a math genius, but it is interesting and unique,

      --
      The Kruger Dunning explains most post on /. http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
    7. Re: No story here, move along by alex4u2nv · · Score: 1

      *8bit. Auto correct on phone made it an 8th.

    8. Re:No story here, move along by tobiasly · · Score: 3, Informative

      The neuroscientists who have been studying his brain seem fairly convinced he's not making it up. Though calling him a "math genius" doesn't necessarily seem warranted (at least not yet... maybe it's a case where formal study will allow him to apply his abilities more specifically?), I don't think they would diagnose him with what they're calling acquired savant syndrome without some evidence.

      Maybe read the book? Even the top negative review seems to give weight to his claim:

      http://www.amazon.com/Struck-G...

    9. Re:No story here, move along by aardvarkjoe · · Score: 1

      I also found this comical link to "End of Pi Found" on some Physics forum:

      http://lofi.forum.physorg.com/...

      *SPOILER ALERT*

      It's a '4'.

      --

      How can we continue to believe in a just universe and freedom to eat crackers if we have no ale?
    10. Re:No story here, move along by mcguirez · · Score: 2

      One might gain an artistic appreciation of his drawings but it is difficult to view this as Mathematics.

      The real story here is that he convinced someone at Houghton Mifflin Harcourt, to publish a book about him.

      I don't doubt that he experiences visual phenomena, perhaps indistinguishable from hallucinations. Although such a unique perspective might conceivably give him an opportunity to understand math in a new way I'm skeptical this occurred. I'm afraid he has no more insight than a nautilus has into the fibonacci sequence.

       

      --
      When you hear hoofbeats, think horses, not zebras
    11. Re:No story here, move along by nospam007 · · Score: 1

      "Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?"

      He sees dead people, all the time.

    12. Re:No story here, move along by khasim · · Score: 1

      Seconded.

      There are 24 paragraphs in the first link. The ONLY mention of ANYTHING about his mathematical "ability" is in paragraph 9.

      He started sketching circles made of overlapping triangles, which helped him understand the concept of pi, the ratio of a circle's circumference to its diameter.

      That's a "savant"? How many kids in high school understand pi?

      After his injury, Padgett was drawing complex geometric shapes, but he didn't have the formal training to understand the equations they represented.Again, how many high school kids have doodled like that?

      And "FORMAL training"? Isn't part of being a savant NOT needing formal training? You discover the concepts on your own based upon your ability to intuit the relationships.

      Srinivasa Ramanujan was a savant.

    13. Re:No story here, move along by geekoid · · Score: 4, Informative

      No, the media calls him math genius because he calls himself a math genius. Also, he believe PI has an end.
      from the neurologist's preliminary report:

      We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic experience and to investigate the neural basis of this phenomenon. In a functional magnetic resonance imaging (fMRI) study, image-inducing formulas produced larger fMRI responses than non-image inducing formulas in the left temporal, parietal and frontal lobes. Thus our main finding is that the activation associated with his experience of complex geometrical images emerging from mathematical formulas is restricted to the left hemisphere.

      --
      The Kruger Dunning explains most post on /. http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
    14. Re: No story here, move along by peragrin · · Score: 2

      I don't know about fried but that was my thought. the injury cross linked his normal "cpu" and vision "GPU" basically using his normal vision processing as a massive floating point processor. Not unlike using your GPU to mine bit coins or do other massively parallel processing.

      --
      i thought once I was found, but it was only a dream.
    15. Re:No story here, move along by Anonymous Coward · · Score: 0

      Perhaps, dipshit, it's because most brain injuries result in significant loss but almost never any kind of improvement?

      Speaking as a guy who had a parent smash his head into the floor, causing significant damage to the Corpus Callosum and thus removing his ability to remember or comprehend the bulk of visual that can't be directly verbalised, this is really quite remarkable.

    16. Re:No story here, move along by khasim · · Score: 2

      Maybe read the book? Even the top negative review seems to give weight to his claim:

      No. None of them do. Most of them repeat the information about being mugged.

      But there isn't a single one of those that specifies HOW he is a "genius" of any kind.

      Can he look at a formula and intuitively draw it?
      Can he look at a drawing and intuitively give the formula for it?

      The simplest question on his "genius" is still unanswered. WHAT does he do that is "genius" level? HOW is it "genius" level?

    17. Re:No story here, move along by sjames · · Score: 4, Insightful

      You mean other than going from a party boy furniture salesman to a student of mathematics specializing in number theory?

      Savantism doesn't mean an ability practically nobody else has (though it can be that), it is an ability that is out of context for the person who has it.

    18. Re:No story here, move along by BiIl_the_Engineer · · Score: 3, Informative

      How many kids in high school understand pi?

      An elite few. Most people simply memorize equations and procedures; understanding never comes into it.

      But still, I'd be impressed if this guy actually did something, like solve an unsolved problem. Sadly, these popular math 'geniuses' and child 'geniuses' never seem to do a damn thing that's truly notable.

      --
      These comments are my own and do not necessarily reflect the views or opinions of my employer or colleagues...
    19. Re:No story here, move along by Charliemopps · · Score: 5, Informative

      I don't know if the guy is full of shit or not... but, I did my own google search.

      I found that:
      1. He wrote a book that was well received about his injury, though complaints were that it was overly wordy. There were several people that claimed to be mathematicians that reviewed it and said his area of specialty was fractal geometry and that he was so specialized it was uninteresting to them. He was basically obsessed with 1 aspect of geometry.
      2. He is an artist, and makes Fractal art. Not that his stuff is that incredible but I doubt a furniture salesman could pull this off. http://fineartamerica.com/prof...
      3. Here's photos of him. One includes his doctor: http://www.struckbygenius.com/...
      4. That doctors name is Darold Treffert who appears to be am expert on Savant Syndrome. http://en.wikipedia.org/wiki/D...

      So it appears to me that the guy actually did develop some Savant abilities. I don't know if he got them from an injury or not. But it appears that those abilities are so specialized that they may not be useful in an academic sense. If he can visualize incredibly complex geometries but can not, for example, do long division, his skill wouldn't really lead him to write a lot of papers.

    20. Re:No story here, move along by sjames · · Score: 3, Interesting

      Under the conditions he specifies, Pi does have an end. He makes it clear he means as seen in the physical world where it is bound by the Planck length. He may or may not realize that mathematicians prefer to have as little as possible to do with the physical world, at least professionally.

    21. Re:No story here, move along by Anonymous Coward · · Score: 0

      The significance here is the more recent discoveries about how the brain works, not his 2002 injury.

    22. Re:No story here, move along by Richy_T · · Score: 2

      My understanding is that advanced maths becomes almost exclusively symbol manipulation. I could intuit a lot of physics stuff and easily attach equations to concepts but when it came to the quantum stuff, it was a totally different story. That could have just been the way it was taught though.

    23. Re:No story here, move along by camperdave · · Score: 3, Funny

      "Can someone explain to me exactly what is so marvelous about what this dude can supposedly "see"?"

      He sees dead people, all the time.

      So does a mortician. Big deal!

      --
      When our name is on the back of your car, we're behind you all the way!
    24. Re:No story here, move along by Richy_T · · Score: 1

      In the physical world, its expression (pi is always constant, of course*) is also affected by gravitational curvature and possibly other effects.

      *For some values of "of course"

    25. Re:No story here, move along by KramberryKoncerto · · Score: 3, Informative

      Sadly, these popular math 'geniuses' and child 'geniuses' never seem to do a damn thing that's truly notable.

      Perhaps except Terrence Tao; a famous math prodigy, who also became an incredibly successful mathematician, "Such is Tao's reputation that mathematicians now compete to interest him in their problems, and he is becoming a kind of Mr Fix-it for frustrated researchers. "If you're stuck on a problem, then one way out is to interest Terence Tao," says Charles Fefferman [professor of mathematics at Princeton University].". Also Erik Demaine, who finished PhD and became a professor at MIT at 20; he has a less impressive history than Tao, but still a fruitful career.

    26. Re:No story here, move along by Anonymous Coward · · Score: 0

      We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures.

      This implies that if you show him an equation written out with its x's and y's, he's able to see the graph of it in his mind's eye. I didn't read much about this ability in the links, so was anyone able to find if this is what is meant?

    27. Re:No story here, move along by Bing+Tsher+E · · Score: 3

      In the physical world, 355/113 is a close enough approximation that almost nobody owns a physical instrument precise enough to need anything better.

      And 355/113 is even easy to remember. One one three under three five five.

      I've never understood why 22/7 gets so much admiration.

    28. Re:No story here, move along by Skarjak · · Score: 1

      I'm with you. As I was reading this, I was asking myself when they'd start telling me how he was a math genius. I understand that his brain has now lost the ability to smooth "frames" together. Wow, some math genius he is. We should be pitying him, not hailing him as a savant. He's now basically playing a terribly optimized videogame 24/7.

    29. Re: No story here, move along by jones_supa · · Score: 1

      Your comment inspired me to take computer graphics to the 8th level!

    30. Re:No story here, move along by Anonymous Coward · · Score: 1

      I'm not sure if it's the same person, but I was watching a documentary where they covered someone with a similar "issue". They were able to see patterns where others could not. Because they could see the patterns, they could describe them to other scientists who could create a model. Imagine being able to look at something an instantly having a model for it, instead of spending years of poking around to haphazardly discover the pattern.

    31. Re:No story here, move along by Anonymous Coward · · Score: 5, Funny

      Says the 6-digit to the 3-digit user ...

    32. Re: No story here, move along by Anonymous Coward · · Score: 0

      He doesn't specialize in jack shit.

    33. Re:No story here, move along by Anonymous Coward · · Score: 0

      I've never understood why 22/7 gets so much admiration.

      Next time someone writes 22/7 on the black/whiteboard in your presence, rub out the /7 and put 2143/ above the 22. Then say their fraction is less than a quarter the accuracy of yours, and write ^(1/4) after it.

      It's not even a matter of remembering a 4 digit number and a fraction easier than two 3 digit numbers. I just alternate counting up in evens and odds alternately, and rely on the power of visualising this rubbing out story for the fraction (pardon the pun).

    34. Re:No story here, move along by Anonymous Coward · · Score: 0

      I just alternate counting up in evens and odds alternately,

      Meant to say: " I just remember to count up in evens and odds alternately"

    35. Re:No story here, move along by genik76 · · Score: 1

      So you have to remember 6 numbers to be able to perform a division giving you pi with 7 digits' accuracy. Seems like a poor deal.

    36. Re:No story here, move along by Rick+in+China · · Score: 1

      Don't be so harsh on the poor guy. He did have one VERY intriguing and wise quote: "There's no such thing as a perfect circle, he said" Can't you identify with that sort of depth and insight? // Like you I had a rant when I read this and was bemused by the story and how it ended with nothing really showing any genius but providing us with a 'wow awesome' title, ranted a bit to my father in Skype, laughed, and we moved on. Suggest everyone does the same :)

    37. Re:No story here, move along by TheRaven64 · · Score: 3, Insightful

      I wouldn't say no one else does it. From his description, it sounds exactly like how the world looks after taking magic mushrooms. It's no surprise that a brain injury can permanently create effects that a psychoactive substance can create temporarily...

      --
      I am TheRaven on Soylent News
    38. Re:No story here, move along by fractoid · · Score: 1

      Thanks for the link!

      1. Those aren't fractals.

      --
      Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
    39. Re:No story here, move along by Anonymous Coward · · Score: 1

      Yeah, there's a lot of big talk about how he's an "intuitive genius specialising in fractals" and yet his art page contains only images generated by curve stitching.

      I have a cousin who's done too many drugs and now thinks he can see angels and the interconnectedness of all things and that he's part of a global shamanistic spiritual uprising. That doesn't make him a maths genius.

    40. Re:No story here, move along by kruach+aum · · Score: 2

      Well, I mean, we never see people make significant life changes after traumatic events. That's why no one converts to Christianity in prison, why middle-easterners don't radicalize after their family is blown up, and why the term "near-death experience" is meaningless.

      wait

    41. Re:No story here, move along by L4t3r4lu5 · · Score: 1

      I am currently in IT. I could apply to university as a mature student (read: Able to pay his own way, so no entry criteria) on any course I wanted. Am I all of a sudden a Physics savant?

      Savantism is an ability beyond that which is expected in the majority of the population, and also without any special instruction or education in the subject matter. It's great that this guy got his life on track and is getting himself educated, but unless he's already capable of doing advanced number theory in his head, he's no savant.

      --
      Finally had enough. Come see us over at https://soylentnews.org/
    42. Re:No story here, move along by sjames · · Score: 1

      It is somewhat less common to develop a talent or aptitude for something they didn't have before, such as math.

    43. Re: No story here, move along by sjames · · Score: 1

      Correct, he specializes in number theeory.

    44. Re:No story here, move along by sjames · · Score: 2

      If you chose IT because physics was beyond you (personally, not humans in general), but one day you slipped on a floppy, hit your head on the edge of a server, then when you woke up you exclaimed "So THAT's what Einstein was saying!", then yes. Otherwise, no.

    45. Re:No story here, move along by Warma · · Score: 1

      As far as I know, that art link does not contain anything that a furniture salesman could not pull off. The drawings don't seem to have any connection whatsoever to their scientific, nonsensical names, and the only thing he seems to do is to draw intersecting lines from and to the vertices of polygons.
      This does not really seem like a savant ability.

    46. Re:No story here, move along by Anonymous Coward · · Score: 0

      you're just jealous of this guy's super powers. I suggest you stop wearing a cape at home and learn to live within your limitations. Seriously. Why does this evoke so much ire?

    47. Re: No story here, move along by ArsenneLupin · · Score: 2

      He doesn't specialize in jack shit.

      Isn't a more polite expression for this santorum?

    48. Re:No story here, move along by cdrudge · · Score: 1

      They look more like spirographs then fractals.

    49. Re:No story here, move along by fractoid · · Score: 1

      I'd classify most of them as curve stitching but I agree, some of them do look like spirograph patterns... man, talk about a blast from the past!

      --
      Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
    50. Re:No story here, move along by Anonymous Coward · · Score: 0

      Thank you for the insightful commentary. It's comments like yours that make slashdot the valuable world wide web resource that it is today. HAND

    51. Re: No story here, move along by Xemu · · Score: 1

      I don't know about fried but that was my thought. the injury cross linked his normal "cpu" and vision "GPU" basically using his normal vision processing as a massive floating point processor. Not unlike using your GPU to mine bit coins or do other massively parallel processing.

      Mining bitcoins in your head just by looking, now THAT would be a savant skill worth having.

      --
      Tell your friends about xenu.net
    52. Re:No story here, move along by Anonymous Coward · · Score: 0

      Nah, you need to remember three numbers: 1, 2 and 3.

      You start at 1. Each digit is repeated 2 times, then add 2. The result hass 2 pars, each of 3 digits. Finally, switch the parts around, and divide..

      113355 -> 355/113.

      Personally, I just remember that:

      Yes, I like a large container of coffee after the heavy lectures involving quantum mechanics.
      Count the letters: 3.14159265358979

      More precision than either 22/7 or 355/113.

      Apart from that, I don't get 22/7. 3.14 is very close to the same precision, and easier to remember, and if that isn't good enough, 3.1415 isn't that much harder (and if it is too hard, just use 3.1414 instead).

    53. Re:No story here, move along by Anonymous Coward · · Score: 0

      If you've got a problem, and no one else can help, if you can find him, maybe you can hire Mr. T?

    54. Re:No story here, move along by Anonymous Coward · · Score: 0

      Except there's no evidence for any talent, except that the guy keeps saying "I see shapes and angles everywhere" which any brain damaged, traumatised fuck could do without being able to add 2+3 successfully.

      Nice story.

    55. Re:No story here, move along by Anonymous Coward · · Score: 0

      Seems the guy is so self obsessed he has interpreted his own fucking brain damage as a "special skill".

      Now that is a fucking amazing story.

    56. Re:No story here, move along by tobiasly · · Score: 1

      You're misinterpreting my response. I very specifically said I agree that there's no evidence that he's a math genius, at least not yet. GP seemed to imply that he was making *everything* up though. Or maybe I misunderstood him too. All I'm saying is that his claimed ability to see things differently than everyone else seems to have credence.

    57. Re:No story here, move along by sheehaje · · Score: 1

      I don't think the amazing thing is what he can see or can't so, or even what is math skills are or aren't.

      The intriguing part (to me) is the mechanics of the brain changing so drastically after an injury. From the little information I've read - his injuries weren't much more than a concussion - yet it's completely changed some functions of how his brain processes information. That's truly amazing to me - and leads me to more questions but mainly these two: Was this ability there all along and somehow was unlocked? Did the injury change the brain in some way to produce an ability that wasn't there already?

      While this case may have no significance to mathematics or mathematicians it certainly does to anyone in the cognitive sciences.

    58. Re: No story here, move along by Anonymous Coward · · Score: 0

      Yes, and his theory of numbers says that pi "physically ends" in a way related to the Planck constant.

      I guess being a savant has to do more with sounding smart than being smart.

    59. Re:No story here, move along by Anonymous Coward · · Score: 0

      If you chose IT because physics was beyond you (personally, not humans in general), but one day you slipped on a floppy, hit your head on the edge of a server, then when you woke up you exclaimed "So THAT's what Einstein was saying!", then yes. Otherwise, no.

      Remind me to condition my brain for this to be the first thing I exclaim whenever I wake up from a coma in some hospital. I just hope someone is there to capture it on their iPhone and put it on FB.

    60. Re:No story here, move along by Richy_T · · Score: 1

      Decimal fractions were not always as familiar to people as they are now. I think the shift mostly occurred in the 60s and 70s with metrication and increasing use of digital calculating devices (calculators and computers)

    61. Re:No story here, move along by sjames · · Score: 1

      And he went back to school majoring in math. RTFA

    62. Re: No story here, move along by sjames · · Score: 2

      And he is correct under the conditions he states along with that.

    63. Re:No story here, move along by Anonymous Coward · · Score: 0

      (Other AC here)... So? Maybe the trauma just made him like math more now. He's unpublished in an undergraduate math major -- that's not special.

    64. Re:No story here, move along by Anonymous Coward · · Score: 0

      His sketches look like spirograph results.

    65. Re:No story here, move along by sjames · · Score: 1

      Well, we do tend to like the things we're good at more than the things we aren't.

    66. Re:No story here, move along by Anonymous Coward · · Score: 0

      You mean other than going from a party boy furniture salesman to a student of mathematics specializing in number theory?

      Savantism doesn't mean an ability practically nobody else has (though it can be that), it is an ability that is out of context for the person who has it.

      Or perhaps our concept of an individuals' ability is a bit overly tied to their circumstances.

    67. Re:No story here, move along by david_thornley · · Score: 1

      Moreover, if he can intuitively draw a formula, or derive a formula from a drawing, that does not constitute mathematical genius. He's not proving anything. It may be a remarkable ability, and it may be useful, but it doesn't sound like mathematical genius..

      --
      "When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
    68. Re:No story here, move along by Anonymous Coward · · Score: 0

      Says the no-digit to the six-digit...

    69. Re:No story here, move along by CmdrTamale · · Score: 1

      Also, he believe PI has an end

      Pi = 10.0 base pi

      Pi = 100.0 base sqrt(pi)

      I have given up on sub and superscripting here.
      --
      "The single biggest problem in communication is the illusion that it has taken place." George Bernard Shaw

    70. Re:No story here, move along by Anonymous Coward · · Score: 0

      We used to call that an acid flashback.

    71. Re:No story here, move along by L4t3r4lu5 · · Score: 1

      But that isn't what has happened. This guy paints / draws geometric shapes, and his visual perception is damaged to the point that he also sees the world this way. He doesn't solve complex formulae in his head, at least not in any meaningful way. We know that there's math in nature (Golden Ratio, for example); If he can pick that out better than most, then good for him. I still wouldn't call him a savant, not until he can explain it in a way others can understand.

      I see Matt Damon's character in Good Will Hunting as an example of a mathematical savant, even though it's a dramatisation. This guy doesn't come close.

      --
      Finally had enough. Come see us over at https://soylentnews.org/
    72. Re: No story here, move along by tolkienfan · · Score: 1

      No, he's not. There isn't any reason to expect that the ratio of radius to circumference of a physical circle is raional, especially if Planck's constant is irrational. There is also no reason to expect such a ratio to be the same for all such "circles", hence no single constant pi. Personally I prefer the purely analytical definition of pi...

    73. Re:No story here, move along by tolkienfan · · Score: 1

      Maybe he gained a delusion of talent.

    74. Re: No story here, move along by sjames · · Score: 1

      How would Planck's constant be irrational? It does, after all, describe an intrinsically quantized world. In that world, there are no circles at all, only polygons with an outrageous number of sides.

    75. Re: No story here, move along by tolkienfan · · Score: 1

      Are you suggesting irrational numbers can't arise in a "quantized" world?

    76. Re: No story here, move along by sjames · · Score: 1

      I'm suggesting that no quantized number is irrational. Pretty much by the definition of quantized. It will necessarily be truncated.

    77. Re: No story here, move along by tolkienfan · · Score: 1

      By that reasoning you could choose units such that all measurements are in exact integers, which is ridiculous.

    78. Re: No story here, move along by sjames · · Score: 1

      What would be ridiculous about using the Planck length as a unit of measure? It would certainly make at least as much sense as a king's foot or an arbitrary division of an incorrect measurement of one planet's size. I would suggest it except that it's an awfully small unit compared to the practical measurements we typically make.

    79. Re: No story here, move along by Anonymous Coward · · Score: 0

      You're confused. Planck's constant is not a unit. I was suggesting that Planck's constant could possibly be irrational (which would, obviously, depend on the unit you are using). Interestingly, my argument did not depend on that at all. But regardless, no unit of length can eliminate the need for irrational numbers. You'd have to also give up at least one of the following:
      1. Orthogonality
      2. Mathematical consistency
      3. The lack, in Physics, of any "special" direction in space

      Also, note that Planck's constant is closely related to Dirac's constant - they are related by a factor of 2*pi. But this "pi" doesn't come from geometry... and you'd find it hard to make the case that it's truly rational.

    80. Re: No story here, move along by sjames · · Score: 1

      The Planck LENGTH is a unit. I believe you are confused. Planck LENGTH != Planck's constant.

    81. Re: No story here, move along by tolkienfan · · Score: 1

      You switched from talking about Planck's constant, saying roughly that it couldn't be irrational, to planck length. But even still, irrational lengths would still exist. E.g. make a square 1x1. What's the distance across the diagonal? It's either irrational or you've given up orthogonality.

    82. Re: No story here, move along by sjames · · Score: 1

      Or you've quantized it. Welcome to the crazy reality of quantum mechanics, where Heisenberg rules the day. The mathematical answer is irrational, but construct such a square and measure it and find that even a 'perfect' ruler truncates the result.

      Planck's constant and the Planck length are related but not the same thing.

      If you're going to argue against a statement, shouldn't you at least know the definitions of all of the words first?

    83. Re: No story here, move along by tolkienfan · · Score: 1

      If you make the statement that the diagonal is quantized, you're either saying you have a measurement problem, or you're throwing out mathematical consistency. I personally think we're much better off keeping the irrational numbers.

    84. Re:No story here, move along by george1101 · · Score: 1

      I must say, it's not every day someone turns into a genius from understanding just one idea. but on that particular day when it happens, extraordinary claims require extraordinary evidence... I don't find it particularly astonishing this man has attributed his ability as a result of brain injury. more on the previous notion, extraordinary circumstance requires extraordinary claims... and in general, circumstances reveal evidence that supports claims. So in my 'Expert' logical opinion 'This ability should not have a vapid basis like the one you presume it has' Albeit nothing is truly vapid across the ENTIRE cognitive spectrum for any one situation. "The ability has to come from somewhere and it has to be provable" You also can't prove ENTIRE cognitive vapidity. because there are no longer any strong cognitive faculties left to make a strong argument. It is what it is. There's a saying that goes around "treat people as if they are as smart as you, unless proven other wise" Do you honestly think the writer thinks you are stupid enough to believe this without any dissemination? It's amazing, I'll give you that. what this guy understands is beyond maths. you could say his visuospatial ability has improved. Normally a person learns mathematics and therefore understanding the limited if not complete applications of mathematics . This is reported throughout history so many times. Newton, remember him? his theory of gravity? In our limited subjective opinion, who are we to him? Using logic is the best way of understanding this discussed phenomena. All such occurrences rely on brain trauma. It speaks for itself but it's not necessarily proven by itself...

    85. Re: No story here, move along by sjames · · Score: 1

      I don't get a choice, that's just how reality is constructed. It didn't ask me if I wanted space-time quantized or not.

    86. Re: No story here, move along by tolkienfan · · Score: 1

      Science is created by man. But some theories are consistent with others. You can't have a physical system with inconsistent math. So, actually, you do have a choice. You choose the theories that are most consistent with theory. Your idea of a physical universe with no irrational lengths would imply untenable consequences. But you can choose to subscribe to it if you wish.

    87. Re: No story here, move along by mcswell · · Score: 1

      Mightn't he be saying that space (at least at that scale) is not flat? Consider a sphere, like the Earth. Then from a point on the surface of that sphere, construct two line segments on the surface at right angles and of equal length, and construct the diagonal on the surface between their ends. Depending on how long the segments are, the diagonal will range from approximately sqrt(2) times as long (for small segments) to 1 times as long (for segments which extend 1/4 of the way around the sphere). That's a space with positive curvature. I suppose the ratio, and the way it changes with as the lengths measured vary, is different for space with a negative curvature, although I admit I can't intuit it...

    88. Re: No story here, move along by sjames · · Score: 1

      Go tell all those physicists out there. I'm sure they'll gratefully bow to your supreme knowledge.

      Sorry, but theory must conform to the evidence as well, and evidence suggests quantized space-time (meaning there is an actual smallest possible distance between two points). When you grow up to be God, you can create one that doesn't work that way.

      I suspect this to be part of the reason mathematicians prefer not to deal in the physical world.

    89. Re: No story here, move along by Anonymous Coward · · Score: 0

      Sounds like someone needs to go go jelly school...

    90. Re: No story here, move along by tolkienfan · · Score: 1

      Where is evidence of quantized space?

    91. Re: No story here, move along by sjames · · Score: 1

      Yo're just going to have to look that one up. This is not the forum to teach you cosmology and quantum physics.

  2. Correlation != Causation by avandesande · · Score: 2

    Perhaps the karaoke did it?

    --
    love is just extroverted narcissism
    1. Re:Correlation != Causation by quantaman · · Score: 1

      Perhaps the karaoke did it?

      Nah, I can't see a positive outcome from that kind of brain trauma.

      --
      I stole this Sig
  3. Tomorrows headline.. by Moheeheeko · · Score: 5, Funny

    Dozens killed or severely injured trying to learn maths.

    1. Re:Tomorrows headline.. by Anonymous Coward · · Score: 1

      Assailants' defense: we were trying to teach him math!

    2. Re:Tomorrows headline.. by geekoid · · Score: 1

      retrophrenology at it's finest!

      --
      The Kruger Dunning explains most post on /. http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
    3. Re:Tomorrows headline.. by K.+S.+Kyosuke · · Score: 1

      Dozens killed or severely injured trying to learn maths.

      The White House will make a public announcement that they're looking for the irresponsible person than unleashed weapons of math destruction on impressionable American youth.

      --
      Ezekiel 23:20
    4. Re:Tomorrows headline.. by BabaChazz · · Score: 1

      I'm somehow reminded of Wowbagger the Infinitely Prolonged...

    5. Re:Tomorrows headline.. by Coisiche · · Score: 1

      Yeah, it's a bit of an out-lier in the spectrum of brain injuries. All I got from mine are ataxia and diplopia which are things I can't see anyone wanting.

    6. Re:Tomorrows headline.. by crackspackle · · Score: 1

      Dozens killed or severely injured trying to learn maths.

      ...Gives new meaning to "rack you brain" for the answer.

    7. Re:Tomorrows headline.. by crackspackle · · Score: 1

      Dozens killed or severely injured trying to learn maths.

      ...Gives new meaning to "rack you brain" for the answer.

      And apparently I didn't hit my head hard enough before I posted that.

    8. Re:Tomorrows headline.. by Anonymous Coward · · Score: 0

      Far better to use those weapons on youth in Asia...

    9. Re:Tomorrows headline.. by camperdave · · Score: 1

      retrophrenology at it's finest!

      So it's not the bumps, it's the divots?

      --
      When our name is on the back of your car, we're behind you all the way!
    10. Re:Tomorrows headline.. by Anonymous Coward · · Score: 0

      sounds like hard to live with, diplopia that is. Is there a practical solution for it (eg. glasses,...?)

    11. Re:Tomorrows headline.. by Anonymous Coward · · Score: 0

      Hey bigmouth: You're being called out (why're you running "forrest"?) http://slashdot.org/comments.p...

  4. Well that's BS.... by Noishkel · · Score: 1

    All I got from a brain injury was a giant cerebral meningioma about a decade later.

  5. Life imitates art: Phenomenon by tepples · · Score: 3, Interesting

    Isn't this the plot of the 1996 John Travolta vehicle Phenomenon ?

    1. Re:Life imitates art: Phenomenon by Anonymous Coward · · Score: 1

      No

    2. Re:Life imitates art: Phenomenon by fustakrakich · · Score: 1
      --
      “He’s not deformed, he’s just drunk!”
    3. Re:Life imitates art: Phenomenon by Anonymous Coward · · Score: 0

      Acquired Savant Syndrome is older than 1996. Uri Geller's claims, for instance. Phenomenon is art inspired by ASS.

      "Life imitating art" is a cool new age pseudo thingy.

      Sociology / memetics / subtle manipulation / inventions is the only way life will actually imitate art.

      Life is basically solid science, discovered or undiscovered.

    4. Re:Life imitates art: Phenomenon by Agent0013 · · Score: 3, Funny

      Doo - Doo - Do Do Do.

      Phenomenon
      Doo - Do Do Do.

      --

      -- ssoorrrryy,, dduupplleexx sswwiittcchh oonn.. -Quote found on actual fortune cookie.
  6. A "Feyn" place to end Pi by tepples · · Score: 0

    Practically, the end of Pi is around 760-some digits, where you start to sound like Herman Cain. At that point, diameters won't be more than a Planck length off.

    1. Re:A "Feyn" place to end Pi by suutar · · Score: 1

      Seems like we could probably stop at about 187 digits, really. The radius of the observable universe in planck lengths (call it X) is about 2.7*10^61, which makes the observable volume (4*pi*X^3) about (8*10^184)*pi cubic planck units. The value of the 186th digit of pi (after the decimal) should only affect the final volume by about 0.7 units; going much beyond that seems unnecessary :)

    2. Re:A "Feyn" place to end Pi by Charliemopps · · Score: 4, Insightful

      Practically, the end of Pi is around 760-some digits, where you start to sound like Herman Cain. At that point, diameters won't be more than a Planck length off.

      If you're using it for the geometry of the physical world, then you'd be correct. Fortunately however, Pi is used for far more than measuring the physical world.

    3. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      ridiculous, That only applies to numbers in base 10

    4. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      Pi is used for far more than measuring the physical world

      As a relation, yes, but the actual numbers for pi are useless outside of the real world.

    5. Re:A "Feyn" place to end Pi by Em+Adespoton · · Score: 5, Funny

      ridiculous, That only applies to numbers in base 10

      Just imagine a number system of base-pi, or possibly base-rad. Of course, then people would be debating how many digits "10" should be approximated to for useful work (like counting your fingers).

    6. Re:A "Feyn" place to end Pi by Deadstick · · Score: 3, Informative

      Indeed. And if you define pi as the smallest positive real number whose cosine is -1, the Planck length becomes immaterial.

    7. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 1

      Yeah, the world is flat after all and we understand 100% of everything right now. Nothing new will be discovered and we will never be wrong.

    8. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      Just imagine a number system of base-pi, or possibly base-rad.

      I confess that I cannot. Please explain how a number system can exist wherein there is only one number that can be defined, or how there can be one wherein the base is arguably not a number at all.

    9. Re:A "Feyn" place to end Pi by scarboni888 · · Score: 1

      Did you even realize that you had Godwinned the thread at this point? ;^)

    10. Re:A "Feyn" place to end Pi by Skarjak · · Score: 2

      I sense some sarcasm in this post, somehow...

    11. Re:A "Feyn" place to end Pi by Wycliffe · · Score: 2

      It's considerably smaller than that.
      63 decimal places can calculate the circumference of the observable universe to an accuracy of one planck length.
      I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.

    12. Re:A "Feyn" place to end Pi by Bryan+Ischo · · Score: 0

      You cannot because it's not possible. A 'base' is the number of unique symbols in the number system. You can't have partial symbols; you can have 3 symbols for base 3, and 4 symbols for base 4, but you cannot have 3.1415xxx symbols for base Pi.

      You might as well ask what it would be like to have a "base yellow" number system or a "base CmdrTaco" number system. Meaningless.

    13. Re:A "Feyn" place to end Pi by lister+king+of+smeg · · Score: 1

      It's considerably smaller than that.
      63 decimal places can calculate the circumference of the observable universe to an accuracy of one planck length.
      I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.

      To build my full scale working model of the universe of course how else are you going to build your turing oracle.

      --
      ---Saying gnome 3 is better than windows 8 not so much a compliment as it is damning with light praise.
    14. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      Why can't I have 3.1415xxx symbols? I certainly can have exactly that many symbols. I may not be able to enumerate them individually but in theoretical mathematics that is no bar to having them.

      Base PI would have 3.1415xxx symbols for each digit with the least significant digit having a value between 0 and PI. A two digit base PI number would have a value from 0 to PI squared and 3 digit number 0 to PI cubed.

      Now actually writing this numbers down might be a serious challenge, or a fun math problem depending on how you look at it but not possible? Come, on, if I can have the square root of -1 I can formulate a representation for base-PI

      Of course I can at this time think of no practical application but they used to say that about base 2 as well.

    15. Re:A "Feyn" place to end Pi by gl4ss · · Score: 1

      so you would have an enumeration system where you can't enumerate. I think you miss the definition of symbol somehow. maybe your harddisk also has half a bit at the end.

      --
      world was created 5 seconds before this post as it is.
    16. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      > Why can't I have 3.1415xxx symbols?

      No problem. Put your 4th finger here on the cutting board, next to the ruler. KSo lemme get a knife, BRB.

      --fyngyrz

      anon due to mod points

    17. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      You tolerate errors of one Planck length?
      Your Ph.D. thesis is rejected.

    18. Re:A "Feyn" place to end Pi by fractoid · · Score: 1

      I can't think of a single practical application that would have any need to calculate a distance that large to that level of precision.

      How about to win a bet? I seem to recall some famous maths or science guy winning a bet as to what the 100 kazillionth digit of Pi was.

      --
      Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
    19. Re:A "Feyn" place to end Pi by Chrisq · · Score: 4, Informative

      You cannot because it's not possible. A 'base' is the number of unique symbols in the number system. You can't have partial symbols; you can have 3 symbols for base 3, and 4 symbols for base 4, but you cannot have 3.1415xxx symbols for base Pi.

      You might as well ask what it would be like to have a "base yellow" number system or a "base CmdrTaco" number system. Meaningless.

      Wrong, you can have non-integral bases, including base Pi. Your positions each represent Pi, Pi^2, Pi^3 etc

    20. Re:A "Feyn" place to end Pi by serviscope_minor · · Score: 3, Informative

      You cannot because it's not possible.

      To say such a thing, you don't understand what maths is truly about on a very fundemental level. I don't mean this in a bad way. Most people don't because despite the supposed maths eduation one gets they omit this important point. I didn't until very recently.

      Maths isn't about "the rules" it's about YOUR rules. You set the rules, and you can set them to be whatever you like. There are generally three results from such an activity:
      1. The rules are inconsistent.
      2. The rules are trivial.
      3. Some interesting patterns emerge.

      (3) is what maths is about. You pick some rules and see where they lead you. The thing is rules are not as passive as they seem. Sometimes once you pick some basic rules, the patterns build and build and build. Sometimes they join up to other patterns.

      A good example is complex numbers. i is not a real thing. It's just an invention. You can essentially say: I wonder what happens if we have this number i such that i*i=-1. Let's say we'll keep the other rules we know and see what happens.

      The result is incredibly rich. Of course, there is no real numer i, such that i*i=-1, but that just plain doesn't matter.

      There are others too. Smeone asked what happens if we have a nonzero numer e, such that e*e=0. I believe those are called dual numers. They're neat but do not have the quite astonishingly all-pervasive richness of complex numbers.

      Likewise with frational powers. You can't multiply a number by itself half a numer of times, or a negative numer of times. That makes no sense. However, you can take the integers and replae them with fractions, real numbers, complex numbers, matrices and so on just for shits ang giggles and see what happens. Naturally if you're working form integer powers as the premise you need to make sure when they degenreate to simple integers you haven't broken your own rules.

      All the rules you know and have seen for such things are merely choices. They are presented as facts because they have by far the most useful and interesting consequenes. But, they're not really facts at all, just choices. It's also nice in that in many cases, it's the most natural way to see what happens when non-integers are used for example as powers.

      This even happens to the extent that the cherished fact 1+1=2 is no fact at all. You get interesting things too when 1+1=0, for example and when 2+2=1.

      So back to number bases. You can have fractional bases simply beause there's no one to tell you you can't. You an if you want: that's the beauty of maths. The question is, can you figure out a way to make it work?

      THAT is maths.

      --
      SJW n. One who posts facts.
    21. Re:A "Feyn" place to end Pi by michelcolman · · Score: 1

      Is there anything not directly pi-related (i.e. not something like "I wonder whether or not the digits of pi are random" or "look how many digits of pi this computer can calculate") in which it's actually usefull to have more than a few hundred digits of pi? Just curious, not being sarcastic.

    22. Re:A "Feyn" place to end Pi by Anonymous Coward · · Score: 0

      You must be a literary savant, seeing the hidden meaning in words!

    23. Re:A "Feyn" place to end Pi by Agent0013 · · Score: 1

      I remember reading an article about the information density in different number bases. Having a larger base, say base 10, allows you to write a big number with fewer digits, like 1022. While having a smaller base, base 2, would take more digits, 1111111110. By multiplying the number of symbols by the number of digits needed (something like that, it was a while ago I read about this) you were able to figure out how efficiently you can represent numbers in any base. It turns out that the most efficient base is between 2 and 3, actually it is base e that comes out as the most efficient base to use. Here is a link with possible references to this question.

      --

      -- ssoorrrryy,, dduupplleexx sswwiittcchh oonn.. -Quote found on actual fortune cookie.
    24. Re:A "Feyn" place to end Pi by St.Creed · · Score: 1

      It's weird, but everytime I read interesting stuff about entropy and information density, "e" pops up somewhere. Weird number.

      --
      Therefore, by the (faulty) logic you're using, you're just a cow with a keyboard - osu-neko (2604)
    25. Re:A "Feyn" place to end Pi by Wycliffe · · Score: 1

      Yeah, I considered adding this to my post as the only practical application but my guess is that even if you wanted
      to simulate the entire universe that you would take shortcuts and never need that precision.
      On a somewhat related note if we are currently living in a simulation and the microscopic stuff is only fully
      simulated when examined closely that might explain certain quantum effects like wave particle duality.

    26. Re:A "Feyn" place to end Pi by tlhIngan · · Score: 1

      Seems like we could probably stop at about 187 digits, really. The radius of the observable universe in planck lengths (call it X) is about 2.7*10^61, which makes the observable volume (4*pi*X^3) about (8*10^184)*pi cubic planck units. The value of the 186th digit of pi (after the decimal) should only affect the final volume by about 0.7 units; going much beyond that seems unnecessary :)

      To be even more dramatic, while the planck length determines the ultimate resolution, you only need 39 digits of pi to calculate the circumference of the observable universe to within the width of a hydrogen atom.

    27. Re:A "Feyn" place to end Pi by Immerman · · Score: 1

      What does the size of the observable universe have to do with anything? Talk about a completely arbitrary limit. We have reason to believe the universe is far larger than what we can observe (and in fact are losing more of the matter of the universe beyond that barrier at every moment), and for practical purposes 5-10 digits is plenty. Neither of those have anything to do with the decimal expansion of number proven to be irrational and non-repeating.

      --
      --- Most topics have many sides worth arguing, allow me to take one opposite you.
    28. Re:A "Feyn" place to end Pi by Bryan+Ischo · · Score: 1

      Well thanks for the well though out response.

      I guess it really comes down to what question is being asked.

      I believe that most people think of "base" as the number of symbols that can be used in a "standard math system" using symbolic representations that can be written and operated on using the same "rules" as in base 10 math, but with a different number of symbols.

      It is true that you can define the rules however you want, so we could even define a system where "base CmdrTaco" has meaning, because we could make the rules be whatever we want.

      But nobody actually means that when they talk about "base N" because it's kind of pointless. Why even ask the question about what it would be like if we could have "base N" if the answer is, "it would be however you want it to be".

      Therefore, I believe that you have misinterpreted the question, by applying the most liberal possible interpretation to the concept of "base".

      I believe an analogy would be if someone asked you "who was the first president of the United States" and you answered "James Bond". And then you explained your answer by saying "Oh I assumed you were asking about who the first president of the United States was in the invented universe I made up in my mind". I mean sure, if we can interpret any question in the most liberal sense possible, then any answer is possible to any question, and that's kind of pointless.

    29. Re:A "Feyn" place to end Pi by Em+Adespoton · · Score: 1

      You cannot because it's not possible. A 'base' is the number of unique symbols in the number system. You can't have partial symbols; you can have 3 symbols for base 3, and 4 symbols for base 4, but you cannot have 3.1415xxx symbols for base Pi.

      You might as well ask what it would be like to have a "base yellow" number system or a "base CmdrTaco" number system. Meaningless.

      You appear to be assuming that a number system must consist of discrete objects (such as fingers) that can be reorganized in interesting ways. That's using integers, but that's only one way to look at the universe.

      If, for example, you went with base yellow, you'd have a very rich number system, which for humans would be an instantly comprehensible Real number system stretching from Red to Violet, with Yellow as the base point. You'd really be basing it on temporal frequency, which would have all sorts of neat results that you wouldn't have to define after the fact, because they'd be a built-in part of the system. So for example, you could say "It's going to be this colour orange out today" and people would know exactly what temperature you were talking about -- in fact, we already use "heat graphs" because they're so much better at conveying quantifiable information in some situations than decimal numbers.

      However, if you've settled on a base of Yellow (think white balance in photography), then you can also use this system to measure differences in weight and even discrete numbers of objects, albeit in a more abstract sense.

      Another place you can see this is in an analog clock. Sure, it's got either roman or decimal numbers on it usually, but you can also think of it as a representation of either Pi or Rad, and the full circle lends itself much better to this than to dividing it up into an infinite number of discrete slices. So when we say "It's ten o'clock" we're actually making a flawed approximation to the actual time, based on the best accuracy we can make with a decimal number system. Using this argument, you can say that using a number system to track time isn't possible, as you can't accurately represent the passage of time with integers. And yet we do it every day.

      The language systems you use (including number systems) heavily influence the way you think and see the world around you. There are some cultures in the world that don't have words for certain objects and concepts -- they get along by using the other concepts to approximate the missing one, or they just don't think about that concept in the first place.

      By painting the box that says "a number system's base must be integral" you are severely limiting the way you observe the world around you.

    30. Re:A "Feyn" place to end Pi by serviscope_minor · · Score: 1

      I guess it really comes down to what question is being asked.

      Indeed. Bear in mind that a lot of maths starts asking silly/funny/strange questions just for the hell of it. Galois invented modular arithmetic in 1832. It's very useful in things like cryptography and error correcting codes, but it didn't become useful in a practical sense until well over 100 years later.

      I believe that most people think of "base" as the number of symbols that can be used in a "standard math system" using symbolic representations that can be written and operated on using the same "rules" as in base 10 math, but with a different number of symbols.

      Pretty much. I believe what you're referring to is generally a "standard positional number system", or more specifically, everything that doesn't fall into the borad definition of having an integer base of greater than 1 is generally referred to as a "nonstandard positional system".

      But nobody actually means that when they talk about "base N" because it's kind of pointless. Why even ask the question about what it would be like if we could have "base N" if the answer is, "it would be however you want it to be".

      Indeed. If one doesn't stick to standard naming, then people get confused and there's little point in confusing people for the sake of it. I'm prepared to say that base-N (where N is an integer gerater than 1) follows exactly the quite simple and elegant rules one expects. Likewise if someone's talking about a "number", I'll generally assume they're talking about probably an integer or a real number unless they specifically say otherwise.

      Anyway, I think my point didn't come across clearly. My point is that things like fractional bases and fractional powers don't inherently amke sense. It's not that you can't do them it's that you haven't invented a way to do them. In this sense you can do whatever you like as long as you invent a way. For number bases, you generally want it to have certain properties:

      1. If you plug in an 10 instead of a fraction, it really ought to look like base 10, otherwise it's basically inconsistent and not interesting. Likewise for all other integers > 1.
      2. You need to be able to represent all real numbers with your system otherwise it's not much use and only works "properly" for integers (except perhaps for the odd degeneracy).
      3. You probably don't want to have special cases (if number is an integer do this else do that) because that's horrible, inelegant and unpleasant, and almost certainly not very interesting.
      4. You probably want it to be able to work with all the things that normal number bases work (e.g. algorithms) automatically and without having to change them.

      Once you have done that, there are two probable paths:
      1. You invent the same thing that everyone else works on. This is quite easy to do for non positive integer powers. In this case you'll eventually find the names everyone else uses and avoid confusion.
      2. You invent something new. To avoid confusion, you'll need to give it a different name.

      So back to number bases. It turns out it's interesting if you simply pick the number of symbols as floor(base)+1. Base 2, 10, ... etc still work perfectly. Multiplication algorithms work fine with no modification. So does addition up until you have to perform a carry at which point it you have to generalise the carry algorithm to suit. An example.

      If you have base pi, then the you'll have 3 symbols like base 3 (0, 1, 2), and the digits will be:
      pi^n, pi^n-1, ..., pi^2, pi, 1. So to compute pi * pi you'd find the representation in base pi. This satisfied by 10: 1 lot of pi + nothing else.

      We're not in modular arithmetic, so using the normal multipliction algorithm, we get: 10*10 = 100.

      Looking back in the table of what each digit means, we get pi^2, so it's consistent with how we expect a number base to work.

      --
      SJW n. One who posts facts.
    31. Re:A "Feyn" place to end Pi by Bryan+Ischo · · Score: 1

      Thank you again for your response, very interesting. And I mean that sincerely, and did also in my previous reply. I feel a little better educated for having read your posts and that's a rare thing on these forums :)

  7. Uh... by K.+S.+Kyosuke · · Score: 5, Insightful

    Padgett dislikes the concept of infinity, because he sees every shape as a finite construction of smaller and smaller units that approach what physicists refer to as the Planck length, thought to be the shortest measurable length.

    So, the bang on the head didn't help him improve his abstract thinking after all. How can someone be an "aspiring number theorist" and dislike the concept of infinity? That's like being an aspiring blacksmith and disliking the concept of tempering carbon steel.

    --
    Ezekiel 23:20
    1. Re:Uh... by Anonymous Coward · · Score: 0

      Disliking something doesn't mean *not believing* in it. I don't like Picasso, but I like postmodernism concepts as an artist. Does that make me less of an artist or more of a historian? Or vice-versa?

    2. Re:Uh... by suutar · · Score: 0

      sounds like he's trying to be a practical mathematician (I made that term up, so if it's supposed to mean something else, my bad) by finding actual numbers for things instead of saying "impractically countable" :)

    3. Re:Uh... by hey! · · Score: 2

      I had a friend who once interviewed R. Buckminster Fuller for his college newspaper, and got into an argument with Fuller over geometry. That took chutzpah, but my friend was on solid ground: Fuller claimed that lines couldn't really intersect because the bits that touched would have to somehow interfere with each other.

      Clearly this visualization-based dislike of intersecting lines didn't hamper his use of the *abstraction*, otherwise Fuller couldn't have functioned as an architect.

      --
      Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
    4. Re:Uh... by Anonymous Coward · · Score: 1

      There are professional mathematicians who not only dislike the concept of infinity but outright deny it. For example they believe infinite set should never be used. It's called Ultrafinitism.

    5. Re:Uh... by K.+S.+Kyosuke · · Score: 1

      To be honest, this kind of reasoning strikes me as incredibly artificial. How much is it different from saying that irrational numbers don't exist because we can't write them? Also, remember Linus Pauling and vitamin C.

      --
      Ezekiel 23:20
    6. Re:Uh... by Richy_T · · Score: 1

      Agreed. And Planck lengths are physics. Mathematics is a useful tool in physics and things in the real world must agree with physical laws (or those laws must be changed [or qualified]) but mathematics is so much more than physics (cue XKCD strip)

    7. Re:Uh... by Bing+Tsher+E · · Score: 1

      The bits that touched would have to share one common point.

      Fuller couldn't grasp that?

    8. Re:Uh... by pz · · Score: 1

      There are a fair handful of constructionists (aka finitists, or number theorists who do not like infinities) who would care to disagree.

      Although I'm not a constructionist, I am related to one by birth, and nearly always find something off-putting about mathematical arguments that rely on infinities. Sure, they're fun to play with, but reasoning about them means you're essentially being fast-and-loose with time, and I've not been convinced that's OK.

      --

      Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
    9. Re:Uh... by K.+S.+Kyosuke · · Score: 2

      But why should dealing with infinities be "essentially being fast-and-loose with time"? What does time, essentially a notion from thermodynamics, have to do with basic mathematics? That just doesn't make any sense to me.

      --
      Ezekiel 23:20
    10. Re:Uh... by Anonymous Coward · · Score: 0

      Most blacksmiths have no need for tempering their work. It is mostly ornamental or simple fixtures like hinges and the like. It is a myth that every blacksmith was a competent bladesmith. A good analogy: tempering is to blacksmiths as microprocessor design is to computer scientists.

    11. Re:Uh... by pz · · Score: 1

      I don't buy the thermodynamic argument. That's an epiphenomenon (i.e., correlation not causation).

      Basic mathematics does not consider time. Nor does it really consider sequential ordering properly until it deals with the notion of state, State begets the field of Computational Theory. Before a proper wrangling of the ideas at the core of Computational Theory (as embodied in Turing Machines, for example), there was a horrific thrashing-about that was particularly inelegant, such as the attempts in First Order Logic to capture the meaning of state.

      Now, when you talk about infinity, you are effectively saying that results from Computational Theory are being computed by a machine that takes zero time to get from one state to the next. Nothing in the physical universe takes zero time, and so infinity is considered to be ill-supported by Nature. That's the crux of the Constructionist objections.

      Now why should mathematics be beyond time? It describes space pretty well. Why should time be exempt?

      --

      Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
    12. Re:Uh... by K.+S.+Kyosuke · · Score: 1

      Now, when you talk about infinity, you are effectively saying that results from Computational Theory are being computed by a machine that takes zero time to get from one state to the next. Nothing in the physical universe takes zero time, and so infinity is considered to be ill-supported by Nature. That's the crux of the Constructionist objections.

      And here I was thinking that some of the most beautiful knowledge in mathematics stemmed from the fact than unlike with trivial mechanical or computational/enumerative reasoning, proper mathematics is able to formulate finite-sized arguments about infinite objects. And you're saying that there are evil people out there who want to take the fun out of it? That's really naughty of them.

      Now why should mathematics be beyond time?

      Because artificial limitations are useless? What if we find that space isn't continuous, will you call for abolishing real numbers or something?

      --
      Ezekiel 23:20
    13. Re:Uh... by Anonymous Coward · · Score: 0

      Hey bigmouth: You're being called out (why're you running "forrest"?) http://slashdot.org/comments.p...

    14. Re:Uh... by Anonymous Coward · · Score: 0

      Hey bigmouth: You're being called out (why're you running "forrest"?) http://slashdot.org/comments.p...

    15. Re:Uh... by Anonymous Coward · · Score: 0

      Hey bigmouth: You're being called out (why're you running "forrest"?) http://slashdot.org/comments.p...

    16. Re:Uh... by Anonymous Coward · · Score: 0

      Hey K.S. Kyosuke ya bigmouth: Yer bein' called out (why're ya runnin' "forrest"?) http://slashdot.org/comments.p...

    17. Re:Uh... by Anonymous Coward · · Score: 0

      But it did help his concrete thinking. Perhaps he ends up doing some work with matrices or computer science. ;)

    18. Re:Uh... by Anonymous Coward · · Score: 0

      sounds like he's trying to be a practical mathematician (I made that term up, so if it's supposed to mean something else, my bad) by finding actual numbers for things instead of saying "impractically countable" :)

      That's called an "engineer"! We make up useful-yet-inaccurate formulas for physical phenomena all the time.

    19. Re:Uh... by Anonymous Coward · · Score: 0

      Because artificial limitations are useless? What if we find that space isn't continuous, will you call for abolishing real numbers or something?

      If you read some of N. J. Wildberger's writings, which go from personal views up to entire alternative Mathematical foundations, you will find an enthusiastic and competent supporter of the constructivist / computational / anti-infinity viewpoint.

      His book on Rational Trigonometry is particularly interesting, as well as his papers and random writings. His position against real numbers, in the preface to the book and also in one of his online PDFs, is very convincing. His rational trigonometry and universal geometry formulas and theorems are solid (not no mention quite useful in my programming job.)

      Overall he has changed the way I think about infinity and uncomputable mathematical entities. I would say he definitely has a point. He has a wealth of Youtube sessions too, where he teaches a great part of Maths, including calculus, without touching infinite sets, "real" numbers and other troublesome fabrications.

    20. Re:Uh... by bbasgen · · Score: 1

      Geometry is the antithesis of infinity. He will be "aspiring" to be a number theorist until he is ready to look at numbers beyond the constraints of Geometry.

    21. Re:Uh... by Anonymous Coward · · Score: 1

      He probably felt that once they intersected in a point, they were no longer 2 lines, but 4 half lines. So from that view point, no 2 lines could ever intersect...

    22. Re:Uh... by Anonymous Coward · · Score: 0

      K. S. Kyosuke: You've been called out (for tossing names) & you ran "forrest" from a fair challenge http://slashdot.org/comments.p...

  8. umm..? by Anonymous Coward · · Score: 0

    A Math Genius would hopefully gain employment as a teacher.
    So 6 years at University would be Bachelor's and working on Master's in Literature.
    And.. if a genius.. would have high probability to do doctorate..??

    FYI.. many can see mathematical patterns, do some homework on Chaos theory. Go try and draw a fractal or two..

    and umm.. Smile dude.. you day will most likely get better.. there is a high proability if YOU smile RIGHT NOW.

    You day WILL get better.

    p.s. the above is MATH.. #MATHS -- See the Maths?

    1. Re:umm..? by avandesande · · Score: 1

      Apparently all you need to teach math with is a baseball bat.

      --
      love is just extroverted narcissism
    2. Re:umm..? by TechyImmigrant · · Score: 1

      Being a math genius does not imply you know how to teach.

      --
      I should use this sig to advertise my book ISBN-13 : 978-1501515132.
    3. Re:umm..? by Anonymous Coward · · Score: 0

      And from the article, you don't need to understand math either.

  9. WTF by Anonymous Coward · · Score: 0

    So a jock turns into a person with supposedly above average math capabilities, nothing out of the ordinary if you are an engineer. Would he still flunk algebra?

    1. Re:WTF by mcvos · · Score: 1

      Apparently you can turn a jock into a nerd by damaging his brain? Suddenly I understand college football.

  10. Graphical artifacts by d1g1t4l · · Score: 1

    This symptom is similar to the problem of a video card with faulty memory.

  11. Rare, but does happen by Anonymous Coward · · Score: 0

    I remember seeing a documentary similar to this. A guy dove into the shallow end of a pool and got brain damage. When he recovered he was a musical genius. There are drawbacks however, if I remember the show he said that seeing musical notes all the time was slowly driving him insane. Though this article does not mention that. [[http://www.businessinsider.com/man-becomes-piano-prodigy-overnight-after-suffering-brain-injury-2012-6]]

  12. the many fragments of infinity by epine · · Score: 1

    He strikes me as being more like David Helfgott and less like Rachmaninoff.

    To a large degree in mathematics, infinity is used to invoke the limiting configuration of an unbounded process (where there is always a next step). This isn't precisely the same thing as believing in infinity itself, or any of its many discrete fragments.

    Meaning in Classical Mathematics: Is it at Odds with Intuitionism

  13. MMA Fighter/Math Teacher by avandesande · · Score: 1

    EOM

    --
    love is just extroverted narcissism
  14. Is he truly a math genius? by BitterOak · · Score: 2

    I would define someone as a "math genius" if they're able to solve previously unsolved problems, and publish results in major, refereed mathematical journals. Has he been publishing papers since his injury, or at the very least, has he been doing well on university level math exams? Nothing in the article seems to suggest this, so I do question the headline.

    --
    If I can be modded down for being a troll, can I be modded up for being an orc, or a balrog?
    1. Re:Is he truly a math genius? by Anonymous Coward · · Score: 0

      Yep. If he isn't considered a math genius by real mathematicians chances are he is not one. And if, despite this, he insists on calling himself one chances are he's an asshat.

  15. Runes baby! by Anonymous Coward · · Score: 0

    All processing in the brain is done with runes. It's evolution. You see things like squares, triangles and circles. I think there are about 30 of them total.
    That's why you think a triangle on top of a square looks like a house. Your brain quickly interprets this set of objects that way.

    Seems like this guy sees things as those runes which is pretty interesting.

  16. The revenge of the geeks by excelsior_gr · · Score: 1

    I bet this is a geek conspiracy to lure football players into self-injury considering an upcoming math exam.

  17. Where? by goosesensor · · Score: 1

    Can I find this bar?

  18. Man Think... math is easy! by MonsterMasher · · Score: 1

    I've been there, and like when I go back. Visually .. it's like lines, a grid is over everything and you know momentum and velocities without need of display.. I drempt the mathematics equation which I understand dictates my life.. in fact. The simple function .. y = 1/x. I added a dimension and connected the two at y=0.
    Simple.. but in my dream!
    .
    It's the very male brain. I know it well.
    .
    For him, it's likely all that's left for now.. depending on other factors he is likely high Autism level for things like sympathy. Not completely devastation, he can learn to work with what he has to .. simulate .. those well enough for public interaction (given the correct support.) And likely most of the rest of his brain will become available in time and work.
    .
    I wish him, and all well.
    .

  19. Extruding it out by Anonymous Coward · · Score: 0

    ... because the editors shape the stories in much the same way as an asshole shapes a raunch locomotive.

  20. That's cool, and... by johnholstein · · Score: 1

    Beer turns me into a love machine....

  21. Errr... by Anonymous Coward · · Score: 1

    Probably the writer of the book is the person who convinced the publisher to publish the book. Unless he was that guy too.

  22. Injury unlocked scamming part of brain by TrollstonButterbeans · · Score: 4, Funny

    His math is unchanged, but it *damaged* the ethical part of his brain and now he EXCELS at marketing and con-artistry and I heard he is now going to law school!

    --
    Priest: "Universe from nothing, no laws of physics, sped up time"+ huge discrepancies. Creationism? No. Big Bang Theory
  23. Who said paroled violent convicts can get work? by Anonymous Coward · · Score: 0

    Math tutor jobs abound!

  24. Lucky him... by Anonymous Coward · · Score: 0

    When I got my brain injury, it just resulted in a coma, memory problems, and unstable moods.

  25. So what math problems has he solved by Anonymous Coward · · Score: 0

    Okay genius can you actually do something useful now, like the rest of us "geniuses" that are being paid $12 an hour are supposed to

    Can you actually DO MATH or is it all vectors spinning in infinity that you have total awareness of that are like a bonghit but not much like a publishable insight

  26. I too dislike infinity by penguinoid · · Score: 1

    Infinity isn't a number; you can't add, multiply, nor divide with it. The only legitimate use I find for it, other than communicating with non-mathematical folks, is as a shorthand for unbounded, eg limit of f(x) as x tends to infinity. I suppose you could say that infinity could be used as an answer to "what is the cardinality of the set of natural numbers", but aleph_0 works too and is unambiguous as to which of the many infinities you mean.

    Some people say that [sum from i=1 to i=infinity of 3*10^i] = infinity. To them I say, [sum from i=1 to i=infinity of 9*10^i]/[sum from i=1 to i=infinity of 3*10^i] = 3, but what is infinity/infinity? So long as you leave your unboundedly large numbers as their formulaic description, you can do maths with it.

    --
    Don't waste your vote! Vote for whoever you want, unless you live in a swing state it won't matter anyways
    1. Re:I too dislike infinity by martin-boundary · · Score: 1
      You're conflating many different notions of infinity into some nebulous single meaning of infinity, which you then deny because the various notions are contradictory.

      Infinity is a placeholder, a word that describes any one of many distinct extensions of finiteness. Think of "infinity" like a variable, "x" that can take many values. Depending upon the value it takes in any given application, it has some properties. In a different application, it has other properties. For example, it can mean the point at infinity in the complex plane, but it could also mean the line at inifnity in the projective plane. Or it could mean one of two symbols that describe the extended value representing sums which are not finite, but whose partial sums are monotonic. It can also mean a cardinality, or an unbounded process.

      Really, to imagine that "infinity" must have a single meaning is to classify everything into black and white, finite and (a single) infinite, good or evil (if you're a constructivist or finitist) etc.

      The best way to think of inifinity is that it's a word that lots of people use to mean different things. The important thing is that in any one case, somebody who uses the word makes clear which meaning is to be required then and there.

  27. an alternative explanation by Anonymous Coward · · Score: 0

    >He is an artist, and makes Fractal art. Not that his stuff is that incredible but I doubt a furniture salesman could pull this off.

    Unless the furniture salesman had access to Google. Then he might find something like Mandelbulb3D and be producing far more impressive stuff in a matter of days.

    Granted, art is not math: the idea of a fractal hand was creative - not seen that before. But the rest of the circles and stuff is very, very basic. At least at first glance. Perhaps the blow to the head gave him compensate-for-blow-to-the-head skills in the form of an interest in art? I suppose he is a kind of performance artist.

    I wish him well though. Brain damage is not nice, and if can make a living somehow that is good.

  28. Your pi isn't like mama used to make by Anonymous Coward · · Score: 0

    I have 3.141592653589793 memorized. The heck would I need 355/113 for?

    Some people are just lazy.

    How to memorize: Physical pattern on the numeric pad. Calculator, keyboard, whatever. Try it. Takes about five passes.

  29. Two links? by Anonymous Coward · · Score: 0

    Is it so that pasting two links to the Slashdot "abstract" makes the news "scientific proof"? New Phineas Gage here or entertainment?

  30. Finite mathematics by Anonymous Coward · · Score: 1

    Any consistent set of rules creates a valid form of mathematics.

    There have been mathematicians and philosophers interested in a kind of mathematics limited to finite processes. That sort of mathematics probably has uses - after all computer calculations are always a finite number of steps.

    His dislike of the infinite implies, to me, that he's relying on some unconscious processes for his intuition and those processes have limitations - that doesn't make them or what they create uninteresting.

  31. So he can see far beyond what CERN can do by quax · · Score: 0

    From the article

    "Padgett dislikes the concept of infinity, because he sees every shape as a finite construction of smaller and smaller units that approach what physicists refer to as the Planck length."

    An astounding ability indeed, given that the Planck length is so many orders of magnitude smaller than visible light, in fact it can't even been studied by our most powerful accelerators.

    As it is in fact the theoretically smallest length scale possible it will actually never be 'seen', no matter how banged up the brain.

  32. He did not necessarly develop any ability by aepervius · · Score: 2

    As said in another post he was a math sophomore. The "furniture salesman" is a red herring, what is important is that he had studied math. Not to put him "down" but he does not appear as interesting once you realize that it is something he studied in university.

    --
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    http://www.amazon.com/gp/product/0345409469/
    visit randi.org
  33. Par for the course by Anonymous Coward · · Score: 0

    > Not sure if it's the same guy

    It's the same guy – if you check Google for "Jason D. Padgett" he uses the same email address in stories directly linked to the guy with acquired synesthesia. Apparently recognizing certain well-known equations and having them trigger images of circles and lines in your head makes you a mathematical genius?

    The whole thing is rife with the pseudo-intellectualism that pervades the art world – from the lack of a related mathematical basis to the original equations (try to find any legitimate evidence that e=mc^2 is a hexagon of hexagons surrounded by triangles), to the lack of fact checking and critical thinking on supposedly scientific websites (like never stopping to think whether he'd really still be in the same grade after 6 years). The only difference between this and visualizing the number 8 as a gray blob with a spoke was being able to convince people that there was a deeper meaning to it.

  34. Finally... by Randall311 · · Score: 1

    Knock some sense into you! I foresee lots of brain injuries heading into finals week. Kids please don't try this at home.

  35. More common than thought by Anonymous Coward · · Score: 1

    I suspect that this is more common than people think. Most of us don't let on because of the type of ridiculing seen right here on SlashDot.

    At a young age I had a brain injury. As a result I lost something that is probably best described as what you are.
    I was also given a medication that was in research at the time. That appears to have sped up my brain, they think by increasing the rate of transmission of nerve impulses.
    Losing that part of me I gain a lack of cohesion which might be thought of an odd gain to you. But that freed up other parts and forced me to cope with the world in other ways.
    I don't think in language. In fact, years later I was shocked to learn as a teen that people do think in language.
    In part I think of things in part very much like he describes but with a lot more mathematics and more than just mathematics.
    I have separate parts that think in terms of probabilities, geometries and calculus as well as what might be equated to a database system. I have two separate language processing systems. I have perfect sensory memory - that is a mixed blessing.
    When I'm all functioning together, or at least enough of me, you don't know I'm any different than you.
    When I'm not I avoid interaction with other people. I've setup my life carefully so I can control this.

    I have never knowingly met someone else who has this but I suspect that is because those of us who are different from the norm don't tend to display it, rather we hide it because as children we learn how brutal normals are to anyone who is different. My IQs for math, memory, logic and language are off the scale. I'm careful not to show that but to keep my display persona within the range of 'bright'. That way the villagers don't try to burn me at the stake.

    I strongly suspect that there are many people like this.

  36. pixilated or pixelated? by Anonymous Coward · · Score: 0

    They're two very separate words, but in this rare case they both fit.

  37. some truth in the bullshit pile? by K10W · · Score: 1

    from personal experience there may be some slight truths in it although most the stuff I've seen on him (came across before this article) looks like he's full of shit. I have diagnosed aspergers, I am high functioning but have savant traits and way above average IQ and it initially became apparent as a small child. I was born at 27weeks @ 2lb1oz and in hospital for 6months at birth, due to mistake of junior nurse who did something she wasn't qualified to do (feed me) my lungs got filled with milk (the tube was supposed to go in the other tube ;) ) and I stopped breathing for 7 to 8min. There is record of all this and parents confirmed they were told there would likely be damage to my brain due to way above the oft quoted 4min barrier as well as optic damage from the oxygen given.

    So it seems the accident may have been the trigger for it although a lot more at play. The traits seem to run in minor form through one side of family all of whom are educated to high degree in maths/engineering/science and work in such fields as well as extensive hobbies within them but I am unusual in it is very exaggerated in me.

    I am able to visualise mathematical and scientific theories in a way but it isn't as he describes. It is more like the same appearing object to sense organ but the conceptual object linked to it tends to have the physics etc of it linked in so I notice things naturally just seeing stuff that many wont without deeper thought. I found my studies easier due to this but it isn't special since anyone can train to do it it just doesn't seem to happen naturally in many cases. The seemingly intuitive nature is just deep familiarity and many many people have that.

  38. Math genius or permanent day tripper? by Anonymous Coward · · Score: 0

    Actually, what he's experiencing sounds similar to what a lot of people report when taking hallucinogenic drugs, especially LSD. Apparently, a filter that most of us have in our brains may have been disabled by the injury. I don't see how that would make him a "mathematical genius" by any stretch. Now, if he's gained the ability to derive Schroedinger's Equation in his head, I'll stand corrected.

  39. Good Movie by BradleyUffner · · Score: 1

    I remember this movie; it didn't end well.

  40. I remember... by vorlich · · Score: 1

    the report of a woman in Perth, Scotland who started to speak with a French accent after a brain injury or a stroke (or both). She could not speak French, she just had ze aczent. She sounded good not at all like the Now Legendary TV show "Allo, Allo" (cultural oblique reference, sorry.), it was difficult not to laugh when she was interviewed on the radio.

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